The easiest solution would be using a maintenance plan task to clean up old backup files. However, you could consider scripting your way out of this, using something like the following script:
--====================================================================
CREATE PROCEDURE [dbo].[usp_DeleteOldBackupFiles]
@path nvarchar(256),
@extention nvarchar(10),
@age_hrs int
AS
BEGIN
SET NOCOUNT ON;
DECLARE @DeleteDate nvarchar(50)
DECLARE @DeleteDateTime datetime
SET @DeleteDateTime = DateAdd(hh, -@age_hrs, GetDate())
SET @DeleteDate = (Select Replace(Convert(nvarchar, @DeleteDateTime, 111), '/', '-') + 'T' + Convert(nvarchar, @DeleteDateTime, 108))
EXECUTE master.dbo.xp_delete_file 0, @path, @extention, @DeleteDate, 1
END
--============================
-- xp_delete_file information
--============================
-- xp_delete_file actually checks the file header to see what type of file it is and will only delete certain types such
-- as database and log backups. I suppose they expanded this to certain types of log files as well but as you say this is
-- not documented by MS. Just be aware that it will not delete just any file type
-- First argument is:
-- 0 - specifies a backup file
-- 1 - specifies a report file
-- (I'm not sure what the difference between a "backup file" and a "report file" is, since you specify the extension of files
-- you're deleting with the third argument.)
--
-- Fifth argument is whether to delete recursively.
-- 0 - don't delete recursively (default)
-- 1 - delete files in sub directories
--====================================================================
Credit: http://www.sqlservercentral.com/Forums/FindPost1034057.aspx
There's also xp_delete_file:
master.dbo.xp_delete_file
Best Answer
The only way would be to restore to an edition of SQL Server besides the express edition, then delete the data that you don't need. Then shrink the database below the 10 Gig limit then backup and restore to your express instance.
If this is for a development machine look at getting a copy of SQL Server Developer Edition. It's usually about $50.00 and doesn't have any limitations like database size. It's only limitation is that you can't use the instance for production use.